The need to improve the STEM field of education causes a feeling of uncertainty in relation to the nature and conceptualisation of STEM education not only among educators, but also among the other participants, including students and policymakers. The topic of this research is the possibility of gradual introduction of STEM education in primary schools in comparison with the countries which started implementing it long ago. When talking about pedagogical innovations, one can rightly question their essential meaning, i.e. whether it is possible to introduce them and what effects they will produce. Some education policymakers think that the introduction of innovations in teaching requires huge financial investments, reorganisation of the entire education system and completely different preparation of teaching staff. This study briefly addresses some teaching innovations which have mainly been experimentally verified, which have already produced positive effects, and which can be gradually introduced in our conditions as well, without any major difficulties. The preleminary research used the following scientific methods: the method of analysis and synthesis of the topic of STEM education and the education which encourages working with gifted and talented students, a survey conducted among the students and teachers in three primary schools in the Republic of Croatia (Split and Osijek) and Bosnia and Herzegovina (Laktaši), and the experimental part (gradual introduction of the STEM field in primary education following the example of the STEM club and the Team for Talented and Gifted Students in the Primary School ‘Mladen Stojanović’ Laktaši. In order to achieve the most complete inclusion of students and teachers in the STEM field of education, this paper presents theories and practical methods and forms of work that, through the organization of extracurricular activities, provide the basic prerequisites for its implementation and the selection of models that can be gradually introduced into the educational systems of the Republic of Croatia and Bosnia and Herzegovina. After the preliminary research, eleven schools from the Republic of Croatia and eleven schools from Bosnia and Herzegovina were included in the research. The sample of teachers who participated in the survey is 119 (one hundred and nineteen) from the Republic of Croatia and 113 (one hundred and thirteen) from Bosnia and Herzegovina, the sample of students is 250 (two hundred and fifty) from the Republic of Croatia and 274 (two hundred and seventy-four) from Bosnia and Herzegovina. The sample of BiH parents is 248 (two hundred and forty-eight). Parents from the Republic of Croatia did not participate in the research even though it was offered to them.